Negative Marginal Densities in Mixed Quantum-Classical Liouville Dynamics

• URL: http://arxiv.org/abs/2512.11174v1
• Date: Thu, 11 Dec 2025 23:36:29 GMT
• Title: Negative Marginal Densities in Mixed Quantum-Classical Liouville Dynamics
• Authors: Kai Gu, Jeremy Schofield,
• Abstract summary: We show that the mixed quantum-classical Liouville equation can violate the positivity of marginal phase-space densities.<n>A negativity index, deviations from positivity, may provide a useful metric for assessing the validity of mixed quantumtextendashclassical descriptions.
• Score: 0.4411658619208916
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The mixed quantum-classical Liouville equation (QCLE) provides an approximate perturbative framework for describing the dynamics of systems with coupled quantum and classical degrees of freedom of disparate thermal wavelengths. The evolution governed by the Liouville operator preserves many properties of full quantum dynamics, including the conservation of total population, energy, and purity, and has shown quantitative agreement with exact quantum results for the expectation values of many observables where direct comparisons are feasible. However, since the QCLE density matrix operator is obtained from the partial Wigner transform of the full quantum density matrix, its matrix elements can have negative values, implying that the diagonal matrix elements behave as pseudo-densities rather than densities of classical phase space. Here, we compare phase-space distributions generated by exact quantum dynamics with those produced by QCLE evolution from pure quantum initial states. We show that resonance effects in the off-diagonal matrix elements differ qualitatively, particularly for low-energy states. Furthermore, numerical and analytical results for low-dimensional models reveal that the QCLE can violate the positivity of marginal phase-space densities, a property that should hold at all times for any physical system. A perturbative analysis of a model system confirms that such violations arise generically. We also show that the violations of positivity of the marginal densities vanish as the initial energy of the system increases relative to the energy gap between subsystem states. These findings suggest that a negativity index, quantifying deviations from positivity, may provide a useful metric for assessing the validity of mixed quantum\textendash{}classical descriptions.

Related papers

• Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines [7.716642023459826]
  Instantaneous quantum quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models.<n>We show that barren plateaus depend on the generator set and the spectrum of the chosen kernel.<n>We identify regimes in which low-weight-biased kernels avoid exponential suppression in structured topologies.
  arXiv  Detail & Related papers  (2026-02-11T17:12:56Z)
• Finite-Size Scaling of the Full Eigenstate Thermalization in Quantum Spin Chains [11.94261497810509]
  The eigenstate thermalization hypothesis (ETH) posits that individual energy eigenstates already appear locally thermal.<n>We perform a detailed exact-diagonalization study of finite-size corrections to these relations in the canonical ensemble.<n>Our results provide a systematic and practical methodology for validating the full ETH in quantum many-body systems.
  arXiv  Detail & Related papers  (2026-02-02T08:43:16Z)
• Impact of quantum coherence on the dynamics and thermodynamics of quenched free fermions coupled to a localized defect [0.0]
  We investigate the non-equilibrium quantum dynamics and thermodynamics of free fermions suddenly coupled to a localized defect in a harmonic trap.<n>We show that initializing the system in a coherent superpositions of energy eigenstates leads to non-classical features.
  arXiv  Detail & Related papers  (2025-08-02T17:21:19Z)
• Quantum and Semi-Classical Signatures of Dissipative Chaos in the Steady State [0.40498500266986387]
  We investigate the quantum-classical correspondence in open quantum many-body systems using the SU(3) Bose-Hubbard trimer as a minimal model.<n>We show that classical dynamical behavior, as quantified by the sign of the Lyapunov exponent, governs the level statistics of the steady-state density matrix.
  arXiv  Detail & Related papers  (2025-06-17T20:21:06Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Semi-group influence matrices for non-equilibrium quantum impurity models [0.0]
  We introduce a framework for describing the real-time dynamics of quantum impurity models out of equilibrium.<n>For a quantum impurity model with on-site two-fermion loss, we compute the spectral function and confirm the emergence of Kondo physics at large loss rates.
  arXiv  Detail & Related papers  (2025-01-31T19:00:42Z)
• Quantum linear algebra for disordered electrons [0.0]
  We describe how to use quantum linear algebra to simulate a physically realistic model of disordered non-interacting electrons.<n>Starting from the block-encoding of a disordered non-interacting Hamiltonian, we describe how to simulate key physical quantities.
  arXiv  Detail & Related papers  (2024-11-01T08:00:10Z)
• From angular coefficients to quantum observables: a phenomenological appraisal in di-boson systems [44.99833362998488]
  Motivated by the growing interest in accessing the spin structure of multi-boson processes, we study polarisation and spin-correlation coefficients in di-boson systems. We show that higher-order corrections of QCD and electroweak type, off-shell modelling, and realistic effects such as fiducial selections and neutrino reconstruction are unavoidable.
  arXiv  Detail & Related papers  (2024-09-25T08:30:54Z)
• A quantum eigenvalue solver based on tensor networks [0.0]
  Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases. This study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.
  arXiv  Detail & Related papers  (2024-04-16T02:04:47Z)
• Exact Numerical Solution of Stochastic Master Equations for Conditional Spin Squeezing [6.824341405962008]
  We present an exact numerical solution of conditional spin squeezing equations for systems with identical atoms. We demonstrate that the spin squeezing can be vividly illustrated by the Gaussian-like distribution of the collective density matrix elements.
  arXiv  Detail & Related papers  (2024-02-04T14:03:42Z)
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination [7.0937306686264625]
  stabilizer operations play a pivotal role in fault-tolerant quantum computing. We investigate the limitations of classically-simulable measurements in distinguishing quantum states.
  arXiv  Detail & Related papers  (2023-10-17T15:01:54Z)
• Simulations of the dynamics of quantum impurity problems with matrix product states [0.0]
  impurity model is a paradigmatic example in the study of strongly correlated quantum systems. We characterize the emergence of the Kondo effect by investigating the model dynamics following a quantum quench.
  arXiv  Detail & Related papers  (2023-04-26T18:00:13Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Noisy induced entanglement transition in one-dimensional random quantum circuits [8.424620634789127]
  We consider a one-dimensional quantum circuit with noisy Haar-random unitary gates. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity.
  arXiv  Detail & Related papers  (2022-03-15T11:15:11Z)
• Breakdown of quantum-classical correspondence and dynamical generation of entanglement [6.167267225728292]
  We study the generation of quantum entanglement induced by an ideal Fermi gas confined in a chaotic cavity. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure.
  arXiv  Detail & Related papers  (2021-04-14T03:09:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.